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Perplex
Perplex
  • Dashboard
Topics
Exponents & LogarithmsRounding & ErrorSequences & SeriesFinancial MathematicsMatricesComplex Numbers
Cartesian plane & linesFunction TheoryModellingTransformations & asymptotes
2D & 3D GeometryVoronoi DiagramsTrig equations & identitiesVectorsGraph Theory
ProbabilityDescriptive StatisticsBivariate StatisticsDistributions & Random VariablesInference & Hypotheses
DifferentiationIntegrationDifferential Equations
Paper 3
Plus
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Perplex

Modelling (Lesson 8/10)

Power Models & Proportionality

1 / 14

Discussion

Every object in the solar system is pulled by the gravitational force ​F​ of the sun, which is given by

​
F=d2km​,
​

where ​k​ is a constant, ​m​ is the mass of the object, and ​d​ is the distance between the object and the sun.

At a given distance, how can we model the relationship between ​F​ and ​m.

Solution:

Since ​d​ is fixed, the quantity ​d2k​​ is constant. Writing

​
F=d2k​m
​

shows a linear relationship between ​F​ and ​m​ of the form

​
F=(d2k​)m+0
​

with slope ​d2k​​ and intercept ​0.


In other words, for any mass ​m, the force ​F​ is always ​m​ multiplied by the same constant ​d2k​.

1 free

Modelling (Lesson 8/10)

Power Models & Proportionality

1 / 14

Discussion

Every object in the solar system is pulled by the gravitational force ​F​ of the sun, which is given by

​
F=d2km​,
​

where ​k​ is a constant, ​m​ is the mass of the object, and ​d​ is the distance between the object and the sun.

At a given distance, how can we model the relationship between ​F​ and ​m.

Solution:

Since ​d​ is fixed, the quantity ​d2k​​ is constant. Writing

​
F=d2k​m
​

shows a linear relationship between ​F​ and ​m​ of the form

​
F=(d2k​)m+0
​

with slope ​d2k​​ and intercept ​0.


In other words, for any mass ​m, the force ​F​ is always ​m​ multiplied by the same constant ​d2k​.

1 free